Eurocodes – failing to standardise safety

Mike Byfield, Cranfield University

The Eurocode approach to partial safety factors

• The structural Eurocodes aim to restrict the probability of the actual resistance of structural components falling below the design resistance to 1 in 845 (approximately 10-3).

•Each member state selects its own M values, which are applied to a whole range of different resistance functions.

• Advantage – Political: It retains the authority of member states to set the safety levels achieved by the codes.

• Disadvantage – structural reliability: The system cannot account for variations in the quality of the design expressions

•CEN have adopted what is known as a “boxed values” approach to M-factors.

The probability of the resistance falling below the design resistance is influenced by 3 factors:Reliability of material and geometric properties

Design expression accuracy

The value of partial safety factor, M

Comparison between poor and high quality design expressions

00

Experimental strength

Pred

icte

d st

reng

th

Series1

Series2

Design expression accuracy

Three different resistance functions have been investigated:

• Tensile resistance of bolts (based on 135 direct tensile tests on 20mm diameter grade 8.8 ordinary bolts)

• Bending resistance of restrained beams (based on 20 tests with restraints selected to produce a worst-case scenario)

• The shear buckling resistance of plate girders (based on 35 plate girder tests)

Examples of variations in design expression accuracy

Design task Probability of actual strength falling below

the design strength

R* Safety factor to achieve the

“target reliability”, existing M

factor in bracketsTensile resistance of

ordinary bolts<10-8 0.95 (1.25)

Bending resistance of restrained beams

4.6x10-6 0.95 (1.10)

Shear buckling resistance of plate

girders

1.0x10-2 1.33 (1.10)

Results from reliability analysis

Conclusions from the reliability analysis

• The most complex design task requires the highest safety factor.

•Reliability variations can reduce safety by leading to over-strength components, transferring failure to connections or columns

•Increasing the boxed value to improve the reliability of plate girder design would not necessarily solve all the reliability problems.

Solution 1

•Determine a M factor for each resistance function. The factor could take the form of a numerical constant incorporated into the design expression

•Designer being largely unaware of the origin of the factor.

•No other safety factors on resistance.

•Problem – politically unacceptable

A practical solution to variable safety levels

•Retain the boxed value system

•Embed a supplementary safety factor into each resistance function.

•The boxed values selected by nation states would merely adjust design economy and target reliability.

Supplementary factor, k =

Where:

M is the boxed value

is the safety factor output from reliability analysis

Thus the design resistance, rd = k rn / M

Solution 2

*R

M

*R

Example

In the case of the plastic moment capacity of restrained beamsk = 1.10 / 0.94 = 1.17The modified design expression would take the form:

0MyplRd.pl /fW17.1M

This would offer a 17% increase in the design moment, whilst still achieving the target reliability.

During the calibration of k factors it may be desirable to adjust the target reliability depending on the consequences of failure.

Variations in reliability using the supplementary safety factors

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

Individual design expressions

Rel

iabi

lity,

Pr(

r<r d

)

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

Individual design expressions

Rel

iabi

lity,

Pr(

r<r d

)

Current variations in reliability